Asymptotic Behavior for Textiles in von-Kármán regime

Georges Griso (1) , Julia Orlik (2) , Stephan Wackerle (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics

The paper is dedicated to the investigation of simultaneous homogenization and dimension reduction of textile structures as elasticity problem with an energy in the von-Kármán-regime. An extension for deformations is presented allowing to use the decomposition of plate-displacements. The limit problem in terms of displacements is derived with the help of the unfolding operator and yields in the limit the von-Kármán plate with linear elastic cell-problems. It is shown, that for homogeneous isotropic beams in the structure, the resulting plate is orthotropic. As application of the obtained limit plate we study the buckling behavior of orthotropic textiles.

Mots clés: Keyword: Homogenization; periodic unfolding method; dimension reduction; von-Kármán orthotropic plate; Energy minimization under pre-strain; buckling under homogenized pre-strain Mathematics Subject Classification (2010): 35B27; 35J86; 47H05; 74Q05; 74B05; 74K10; 74K20

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Georges Griso, Julia Orlik, Stephan Wackerle. Asymptotic Behavior for Textiles in von-Kármán regime. 2019. ⟨hal-02422192⟩